Diffusiophoresis-Driven Stratification in Pressure-Sensitive Adhesive Films from Bimodal Waterborne Colloids

The uses of pressure-sensitive adhesives (PSAs) are wide ranging, with applications including labels, tapes, and graphics. To achieve good adhesion, a PSA must exhibit a balance of viscous and elastic properties. Previous research has found that a thin, elastic surface layer on top of a softer, dissipative layer resulted in greater tack adhesion compared with the single layers. Superior properties were achieved through a bilayer obtained via successive depositions, which consume energy and time. To achieve a multilayered structure via a single deposition process, we have stratified mixtures of waterborne colloidal polymer particles with two different sizes: large poly(acrylate) adhesive particles (ca. 660 nm in diameter) and small poly(butyl acrylate) (pBA) particles (ca. 100 nm). We used two types of pBA within the particles: either viscoelastic pBA without an added cross-linker or elastic pBA with a fully cross-linked network. Stratified surface layers of deuterium-labeled pBA particles with thicknesses of at least 1 μm were found via elastic recoil detection and qualitatively verified via the analysis of surface topography. The extent of stratification increased with the evaporation rate; films that were dried slowest exhibited no stratification. This result is consistent with a model of diffusiophoresis. When the elastic, cross-linked pBA particles were stratified at the surface, the tack adhesion properties made a transition from brittle failure to tacky. For pBA without an added cross-linker, all adhesives showed fibrillation during debonding, but the extent of fibrillation increased when the films were stratified. These results demonstrate that the PSA structure can be controlled through the processing conditions to achieve enhanced properties. This research will aid the future development of layered or graded single-deposition PSAs with designed adhesive properties.


■ INTRODUCTION
Polymer films have numerous applications, including pressuresensitive adhesives (PSAs) and protective coatings. The deposition of films from polymer colloids dispersed in water (i.e., latex) reduces the emission of volatile organic compounds (VOCs) 1 when compared with processes using organic solvents as a carrier. However, volatile plasticizers and coalescing aids in waterborne coatings and adhesives contribute substantially to indoor air pollution. 2 Hence, there is a continued need for materials development to achieve target properties without environmental damage. One promising strategy to eliminate VOCs is to mix waterborne colloids of different types to make a nanocomposite film. For instance, a mixture of film-forming colloids and hard fillers is often used in coatings. 3,4 In PSA films, which are the focus of this present work, mixtures of particles with differing gel contents, 5 molecular weight distributions, 5,6 and sizes 6,7 have been explored as a way to adjust the adhesive properties.
PSAs adhere to nearly any surface under the application of light pressure and have applications ranging from tapes, labels, and bandages to graphics and mechanical joints in aircraft. 8,9 For optimal adhesive performance, PSAs require a delicate balance between viscous properties to dissipate energy during debonding and elastic properties to support stress. Hence, adhesive properties depend strongly on the molecular weight distribution, entanglement molecular weight, and cross-linked network. 10−12 There is some evidence in the literature that a gradient (or step) in the composition of PSAs (and hence their molecular and viscoelastic properties) can be used to tailor and optimize the adhesive properties. 13−17 One way to achieve gradient compositions is through a multilayered structure achieved via multiple depositions. The casting of multiple layers on top of one another and the lamination of layers are both technically possible, but such methods can be time-consuming, energyintensive, and expensive for manufacturers.
Two examples of PSA bilayers in the literature are inspirational to the present research. Carelli et al. 13 studied the tack adhesion of bilayer films composed of a more elastic layer and a more dissipative layer in each of two configurations. The use of bilayer systems allowed the surface to have different viscoelastic properties to the bulk. When using a high energy adherend surface (in their case, steel), they found that having a thin elastic layer on top of a thicker dissipative layer increased the work of adhesion by ca. 30%, when compared to the individual components on their own. The presence of an elastic surface layer also altered the debonding mechanism, transitioning it from cohesive to adhesive failure. In other work, Wang et al. 17 likewise found that just a thin elastic surface layer applied on top of the bulk adhesive could be used to tune the tack adhesion. Specifically, they observed an increase in the work of adhesion for a bilayer containing a 3 μm surface layer of a stiffer, higher modulus adhesive on top of a 49 μm adhesive underlayer.
In the work of both Carelli et al. and Wang et al., it was found that a stiffer, more elastic-like surface layer on top of a softer, dissipative layer improved the adhesion. Contrary to this finding, other groups have shown that inverting this orientation can improve adhesion. 14−16 Díez-Garcia et al. 16 found that casting a liquid-like layer on top of a more solid-like layer allowed for fibrillation to occur during debonding, as was shown by the lengthened stress plateau in probe tack curves, which increased the adhesion energy.
In the prior work reviewed here, the benefit of using bilayer adhesives to tune the properties and to improve the performance of a PSA has been shown. The adhesion properties of bilayer (or multilayer) PSAs ultimately are highly sensitive to the fine balance of viscoelastic properties of each layer. To date, the fabrication of bilayer (or gradient) structures used the deposition of two (or more) separate layers. A far more attractive process is to have two or more different types of particles within the same colloidal dispersion (e.g., a mixture of viscous and elastic particles). During the evaporation of water, the particles could then separate, effectively forming a two-layered or graded structure from a single film deposition, in which the sublayers run parallel to the substrate.
The separation of particles into layers is known as stratification. There have been numerous reports of experiments and simulations of stratification in colloidal films, 18−35 as has been outlined in review articles. 36,37 The distribution of individual particles in a drying film of initial thickness, H, can be defined by the Peclet number, Pe.
Pe describes the competition between the speed of the descending film/air interface as water evaporates at a velocity, E, and the rate of diffusion of the particles away from the high concentration region just below the film/air interface, typically found for dilute colloids from the Stokes−Einstein diffusion coefficient, D SE . (At higher colloids content, particle crowding affects the diffusion coefficient.) The initial state is illustrated in Figure 1a. Pe is given quantitatively as For the case that Pe > 1, the evaporation of water is fast compared to particle diffusion, and hence the particles are trapped by the descending film/air interface, accumulating at the top surface. For fast diffusers, Pe < 1. The particles can outrun the descending interface to yield a more homogeneous distribution of particles during drying. If two differently sized particles are mixed together into a single dispersion (i.e., large (L) and small (S) particles) and have Pe L > Pe S > 1, the stratification of small particles on the top surface was discovered in both experimental and computational work, [20][21][22][23][24][25][26][27]33 as is illustrated in Figure 1b.
Sear and Warren 28 and later Sear 29 developed a model of diffusiophoresis to describe the stratification of small particles (or polymer coils) to the top surface of larger colloidal particles. Diffusiophoresis is the motion of one species in response to the concentration gradient of another. Considering hydrodynamic effects, Sear and Warren 28 argued that the stratification is driven by a concentration gradient of small particles that drives the motion of larger colloids downward ( Figure 1c) to reduce the interfacial free energy at the interface between the large particles and the colloidal dispersion. Sear and Warren found qualitative agreement with a model from Zhou et al., 33 but by including the solvent backflow, they found that previous models overestimated the downward velocity of large particles, suggesting stratification would be less pronounced than expected. Sear's model 29 considered the impact of a jammed layer of small particles below the descending film/air interface. For sufficiently high volume fractions of small particles, ϕ S , the small particles form a jammed, solid-like structure that moves downward during water evaporation. For stratification to be observed, the downward diffusiophoretic velocity of the large particles must be greater than the velocity of the jammed layer, such that they can escape the descending film/air interface. If the initial volume fraction of small particles is too high, stratification cannot occur. It has also been shown that stratification is suppressed when the total volume fraction of particles is increased to higher values. 25 By assuming the Figure 1. An illustration of stratification driven by diffusiophoretic motion (a) of a large (blue) particle down a gradient of smaller (yellow) particles, starting from an initially homogeneous mixture of particles (b). The final mixture can be either stratified or nonstratified (c). volume fraction of packed particles in the jammed layer, ϕ jam , to be 0.64 (the random packing fraction), an approximated upper limit for the volume fraction of small particles if stratification is to occur was found to be ϕ S = 0.2. Above this limit, the downward diffusiophoretic velocity of large particles is too slow, and they too will become trapped at the film/air interface. In the works of Sear and Warren and Sear, particle interactions are neglected, and it is assumed that R L ≫ R S . The boundary condition between stratified and homogeneous regimes is given by Sear and Warren 28 as = Pe 2 S S 1 (2) for which Sear proposed the upper limit due to jamming as Experimental tests of the Sear and Warren and Sear models are available in the literature, 24,30,31 showing some agreement with the models.
More recently, Rees-Zimmerman and Routh 27 developed a diffusion−diffusiophoresis model that accounts for the diffusion of small and large particles, diffusiophoresis effects, and the incorporation of particle-interaction terms in a drying bimodal colloidal film. They showed that to achieve small-ontop stratification arising from a downward flux of the larger particles, diffusiophoresis must be included in the model. Without it, large particles accumulate at the top surface. They suggested that diffusiophoresis must be combined with crossinteraction effects (as used by Zhou et al.) to achieve stratification. In the present work, the map from the Sear and Warren model is used because it allows a straightforward comparison to experimental data.
Typically, the intention of stratifying colloidal films is to adjust the properties of the surface compared to the bulk material. To this end, there have been several experimental studies showing how stratification can be applied to tune properties. Examples of properties include surface wetting, 30 abrasion resistance, 38 antibacterial properties, 39 blocking resistance, 40 and nanopigment 41 and metal nanoparticle 42 distribution. Despite these numerous examples, there is no prior work purposefully applying colloidal stratification mechanisms to optimize adhesive properties.
In this work, we studied the stratification in waterborne PSAs containing a mixture of small poly(butyl acrylate) (pBA) particles with larger, adhesive particles to investigate whether a gradient in properties can be achieved through a single film deposition and how the resulting structure influences the adhesive properties. Two types of mixtures were prepared, containing pBA particles either having no external covalent cross-linker or else having an added cross-linker to achieve extensive cross-linking of the intraparticle polymer chains. Thus, we compare the effects of viscoelastic particles and fully elastic particles. We used ion beam analysis to establish the distribution of small particles near the surface, thereby enabling some quantification of stratification. Atomic force microscopy provided complementary information about the surface morphologies. This research aims to correlate the macroscopic tack adhesion properties with the microscopic stratified structure.

■ RESULTS AND DISCUSSION
Characterization of Components. The characteristics of the components used to prepare colloidal mixtures are presented in Table 1. Data include the molecular weight, M w , polydispersity (Đ), and Z-average particle radius, R, along with the corresponding polydispersity index (PDI). One type of pBA particle contained no added cross-linker (hereafter called pBA 0 ). The other type of pBA particle contained 25 mol % ethylene glycol dimethacrylate (EGDMA) as a cross-linker (called pBA 25 ) Two mixtures were prepared: (1) a standard acrylic PSA copolymer (called PSA2) with pBA 25 and (2) PSA2 with pBA 0 . The PSA2 and pBA dispersions (both with a solids contents of 20 wt %) were mixed in a volume ratio of  43 which had a gel content of 63 wt %. b Because the gel content is 100%, the molecular weight of pBA 25 could not be measured. c As reported by van der Kooij et al., 44 the gel content within pBA 25 is 100%. 3:1, yielding volume fractions for the small and large particles of ϕ S = 0.05 and ϕ L = 0.15, respectively. The total volume fraction, ϕ total , was 0.20.
The weight-average molecular weight for the sol components of pBA 0 is far above the entanglement molecular weight of M e = 25000 g/mol 45 for pBA, which means that there will be some viscoelasticity from the entangled polymer chains. PSA2 likewise has a high molecular weight, M w = 259000, and a low glass transition temperature, T g , that will impart viscoelasticity at room temperature. Because of the extensive cross-linking of the intraparticle polymer chains in pBA 25 , resulting in 100% gel, the particles can be thought of as fully elastic, nondeforming spheres. In Figure 2 an atomic force microscopy height image of the surface of a brittle pBA 25 film is shown. Particles have undergone minimal deformation or coalescence, showing random packing with some limited hexagonally packed structures. Because of the brittleness of the material, it is not possible to conduct adhesion or rheological measurements on the pBA 25 material.
To characterize the adhesion properties of PSA2 and pBA 0 , probe tack analysis was used. During a tack test, a spherical probe is brought into contact with an adhesive film and then retracted at a constant speed. The force required to withdraw the probe from the film is obtained as a function of distance and used to produce a stress−strain curve. Presented in Figure  3 are stress−strain curves for PSA2 and pBA 0 . Both samples have a similar maximum stress and initial slope, suggesting similar wetting characteristics and elastic moduli. The fibrillation behaviors are significantly different for PSA2 and pBA 0 . There is a lower fibrillation plateau for pBA 0 that remains steady with increasing strain, in contrast to the obvious increase in stress with strain for PSA2, which is known as strain hardening. 46,47 With strain hardening, a greater force is required to strain the fibrils when they are stretched farther. Strain hardening is common in optimized adhesives that include some light chain cross-linking to impart rubber elasticity. 11 From the analysis of the area under the stress−strain curve, the work of adhesion, W adh , for PSA2 is 146 ± 9 J m −2 , which is greater than 119 ± 5 J m −2 that was found for pBA 0 . As is expected for a standard adhesive, PSA2 has the superior properties. Its strain hardening is consistent with the observed gel content, indicative of some cross-linking.
To explore further the linear viscoelastic properties of PSA2, pBA 0 , and the mixtures, rheometry was performed using a frequency (f) sweep at 25°C, over frequencies comparable to the conditions of the tack tests. Full data showing G′ and G″ are presented in Figure S1 of the Supporting Information. For the correlation of results, it is best to study the viscoelasticity at the frequency corresponding to an initial strain rate of the probe tack test: 30 s −1 . Selected rheological measurements at f = 30 Hz are presented in Table 2, with data for the mixtures that will be discussed later in the results. There are also data at f = 1 Hz, corresponding to the time scale for the bonding of the probe to the PSA. The rheology of PSA2 and pBA 0 showed viscoelasticity that is attributed to entangled, high-M w chains. Following a Soxhlet extraction, both types of particles were found to have a high-M w sol component within a gel network, which will dissipate energy upon deformation.
At the frequency of the probe tack tests, the storage modulus, G′, is slightly larger for PSA2 than for pBA 0 , which is expected because pBA 0 is poly(butyl acrylate) without any optimization. The difference in G′ is not however significant, which is indicated by the agreement in the initial slopes of stress versus strain in Figure 3.
The Dahlquist criterion 48 for tack adhesion (ca. 0.1 MPa) provides a rough upper limit of G′ to achieve good wetting of a surface by an adhesive. At the bonding frequency of the probe tack tests, 1 Hz, G′ values for PSA2, pBA 0 , and their mixture, PSA2 + pBA 0 are comparable to the criterion upper limit. This explains the good tack adhesion demonstrated for PSA2 and pBA 0 in Figure 3 and also indicates good wetting and adhesion for the PSA2 + pBA 0 mixture. For the PSA2 + pBA 25 mixture, G′ is well above the criterion, suggesting this material will not wet the probe sufficiently to achieve good adhesion.
Soxhlet extractions found that the gel content is 29 wt % for PSA2 films and 85 wt % for pBA 0 . Although no ethylene glycol dimethacrylate cross-linker was added during the synthesis of the pBA 0 particles, a high gel fraction was found via the Soxhlet extraction. There are two explanations for this unexpected result. One, it is possible that intramolecular chain transfer occurred during the reaction (so-called "backbiting"), in which a midchain radical is formed. 49,50 This reaction produces branching and occasional covalent cross-links between chains. Two, entanglements of long pBA chains will create physical entanglements. During the Soxhlet extraction, free polymer chains must reptate through the swollen gel network and entangled chains in the samples (approximately 1 mm thick). Any branched chains will diffuse more slowly than linear chains.
The Soxhlet extraction was run for 24 h (8.6 × 10 4 s), but the time scales for swelling and mutual diffusion of the solvent and polymer chains in the network could be even longer, considering typical diffusion coefficients for polyacrylates 51 on

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pubs.acs.org/acsapm Article the order of 1 × 10 −14 cm 2 /s for comparable molecular weights and temperatures. Thus, it seems fair to conclude that some non-cross-linked (possibly branched) chains in the pBA 0 films will remain entangled during the Soxhlet extraction and contribute to the measured gel content. In comparison, there is dense covalent cross-linking in the pBA 25 particles (with added cross-linker), resulting in 100% gel content with a low molecular weight between cross-links leading to a high elastic modulus. Deplace et al. 52 proposed that the easily measurable quantity, tan(δ)/G′, can be used as a predictor of the extent of fibrillation. Fibrillation requires a sufficiently high dissipative component represented by tan(δ). Their research found that significant fibrillation occurs only above a tan(δ)/G′ = G″/G′ value of 5 × 10 −6 Pa −1 . 52 Other work has found fibrillation at values greater than 3 × 10 −6 Pa −1 . 53 It is important to note that there is no universally accepted value of tan(δ)/G′ that represents a transition to a well fibrillating material. Values should be used to compare samples relative to a given set, under consistent experimental conditions. The value of tan(δ)/ G′ for PSA2 is greater than pBA 0 , which explains why its fibrillation is greater than for pBA 0 , as was already shown in the probe tack results in Figure 3. There is significant strain hardening of PSA2, with a plateau stress that is much larger than found for pBA 0 . Both films begin to fail at a strain of 15, with much cleaner probe detachment (abrupt drop) for PSA2 than for pBA 0 . Overall, the fibrillation (and general adhesive performance) of PSA2 is better than for pBA 0 .
Diffusiophoretic Speed. The downward diffusiophoretic speed, U, of the large particles is the speed with which they move away from the film/air interface, due to the concentration gradient of small particles. U can be estimated using eq 4, from Sear and Warren 28 · U E Pe S S (4) where the parameters have each been previously defined.
The values for U calculated using eq 4 are presented in Table 2 to give an indication of whether downward diffusiophoresis of large particles is likely to outpace the interface motion from the evaporation of water. For U > E, large particles can escape the descending film interface, leading to the stratification of small particles on the top surface. If stratification is expected based on the relative values of E and U, then "yes" is written in the final column. Otherwise, "no" is written.
To produce samples with a range of Pe S , film formation conditions were changed, as listed in Table 4.
From the values presented in Table 3, the expectation of whether stratification will occur is inferred. Stratification is more likely to occur when Pe S has a higher value, which is consistent with prior experimental work. 30,36 For Pe S = 19, E ≈ U, and it is a borderline case for which some weak stratification could occur.
Stratification of Cross-Linked, Elastic Particles (pBA 25 ). In the first round of experiments, a mixture of pBA 25 and PSA2 particles was used. In this mixture, the small particles have fully cross-linked intraparticle polymer chains, and can be thought of as elastic.
Surface Morphology. AFM height and adhesion images of the top surface of films formed under conditions of three different Pe S are shown in Figure 4. Height images show surface topography, whereas adhesion maps show a signal related to the relative tip/sample detachment force. The sample with Pe S = 80 (high evaporation rate) shows almost complete surface coverage of the small particles. Image analysis of the small particles provides an approximate particle radius, R, of 50 nm, which is consistent with dynamic light scattering measurements of pBA 25 particles. For Pe S = 19, there is some enrichment of small particles at the surface, but without the total coverage seen for the Pe S = 80 sample. There are also regions where the small particles are covered by a smooth layer of coalesced particles, likely to be PSA2. Finally, the film formed with Pe S = 2 shows a mostly smooth surface in AFM, with no small particles visible. This structure suggests a depletion of small particles at the top surface and good coalescence of the softer PSA2 particles at the surface. The images point to small particle stratification for samples with Pe S = 80 and 19, but not for Pe S = 2.
AFM only provides information about the surface structure of films and is subject to identification of the phases. Elastic recoil detection (ERD), which is a type of ion beam analysis,  ACS Applied Polymer Materials pubs.acs.org/acsapm Article was used to obtain quantitative depth profiles of the small pBA 25 particles labeled with deuterium. 54,55 ERD Depth Profiles. ERD was conducted to determine the hydrogen and deuterium distribution in the top few micrometers of the films. The small pBA 25 components are deuterium-labeled, allowing them to be distinguished from the large component that was free of deuterium. In ERD, incident 4 He + ions forward recoil hydrogen and deuterium (D) atoms upon collision. The energy of the atoms upon detection is used to determine the mass and depth of the forward recoiled atom into the surface. Because of its greater mass, D is forward recoiled from the surface at a higher energy than H. The counts of the higher energy edge of the peaks are a measure of the concentration of each element at the top surface of the film. As 4 He + ions penetrate farther into the film and recoiled H and D travel through the film on their exit, energy is lost. Therefore, the energies of forward-recoiled H and D are reduced, leading to a spectrum of energies for each element. These spectra are used to extract a depth profile of the H and D concentrations. In our experiments, the maximum depth probed was 2 μm, out of an expected dry film thickness of 200 μm.
In Figure 5 we present normalized energy spectra and the corresponding fits for the three samples. The counts of recoiled ions were normalized by the total counts below an energy of ca. 600 keV (corresponding to forward scattered He) to account for small differences in the charge collection and to allow for a more suitable visual comparison of the spectra. The full spectra of the original data, without normalization, are presented in Figure S2. Figure 5 also presents the D depth profiles that have been found through data analysis.
Simply by looking at the energy spectra in Figure 5a for the three samples analyzed with ERD, a difference in the deuterium distributions can be seen. The relative amount of deuterium at the surface (at the front edge of the D peaks, around 1300 keV) increases as Pe S is increased. The counts decrease at the lower energies, which means that the D fraction is lower beneath the surface layer. A greater D fraction at the surface is explained by more of the small, cross-linked particles (pBA 25 ) being stratified onto the top surface.
In the D depth profiles in Figure 5b, for the sample with Pe S = 80, there is a higher D concentration at the surface, with a two-step profile that decreases to the bulk concentration after ca. 1 μm. The film with Pe S = 19 likewise shows enrichment by the small deuterated particles. Both films have an enriched concentration of deuterium (and hence pBA 25 small particles) to depths of ca. 1 μm from the surface, which is consistent with the expectation of the diffusiophoresis model in Table 3. For the sample with Pe S = 2, in contrast, the D concentration is uniform with depth. A single slab representing the random mixture is used to fit the data. A slight enrichment of the hydrogen concentration�from 48.4 to 55 wt %�was required to fit the spectra. This brings the concentration of hydrogen in this simulation close to the concentration in PSA2, indicating that the film surface could be enriched in large PSA2 particles. The deuterium concentration for this sample is constant for the entire probed depth, indicating no stratification of the small particles. These depth profiles are consistent with the AFM image analysis. The stratification of small particles has been controlled simply by changing the evaporation rate of water during the film formation. The end-user can control the stratification, depending on the desired adhesive properties, which are presented in the next subsection.
Probe Tack Adhesion. According to prior work on bilayers, a thin, elastic surface layer is expected to increase tack adhesion. 13,17 Probe tack curves for PSA2 + pBA 25 mixtures with three values of Pe S are presented in Figure 6 and  compared to the original PSA2. Significant differences in the curves are visible as a function of Pe S . In all cases, the fibrillation plateau do not extend as far for the PSA2 sample. For pBA 25 with Pe S = 80, the initial slope is higher than PSA2, which is explained by a higher modulus arising from the enrichment of elastic particles. There is a remarkably high value of the plateau stress, σ plateau , compared to PSA2, which means that a greater stress is needed to extend the fibrils. For Pe S = 19, there is similarly a higher initial slope (suggesting a higher elastic modulus), but the fibrillation plateau is not as well-defined as for Pe S = 80. The fibrils lack some of the extensibility of the higher Pe S mixture, although the plateau stress is initially high. For the sample with Pe S = 2, brittle failure is seen, with no fibrillation plateau, but with a higher initial slope and maximum stress.
The work of adhesion, W adh , is a measure of the total amount of energy (per unit area) required to debond the probe from the adhesive surface. The plateau stress, σ plateau , indicates the average stress required to extend the fibrils. Both of these properties are presented in Figure 7. Both properties increase in value as the Pe S is increased. The samples that have stratified (Pe S = 19 and 80) have values that are greater than found for PSA2 (shown with the dashed line.) The sample that has not stratified (Pe S = 2) has the lowest value of W adh and no measurable σ plateau .
Insight into these results can be provided by the rheological analysis of a PSA2 + pBA 25 mixture. To achieve a random mixture throughout the bulk material for rheology, the sample was formed by drying slowly, such that the two populations of particles were randomly mixed in the bulk material. In this mixture, tan(δ)/G′ = 1.2 × 10 −7 Pa −1 , which is a factor of 10 less than for PSA2 on its own. The implication is that with a random distribution of pBA 25 particles in the Pe S = 2 adhesive, fibrillation is inhibited because the bulk of the film does not have a sufficiently strong viscous component. G′ for the random mixture, meanwhile, is a factor of 10 greater than for PSA2. This is expected for a composite with the addition of a component with a higher elastic modulus. 3,4 The value of G′ for the PSA2 + pBA 25 mixture exceeds the Dahlquist criterion for tack adhesion. 48 This fact explains why brittle adhesive failure is observed when Pe S = 2. According to the ERD analysis of the Pe S = 2 sample, the surface composition is similar to the PSA2 adhesive, which suggests that the elastic pBA 25 particles are distributed throughout the bulk of the PSA film. However, with a high Pe, when there is an elastic layer stratified at the surface, the bulk of the film is less enriched by the elastic particles, and the adhesion properties have an increased value. This result is consistent with previous research 13,17 that showed the benefits of a thin elastic layer on the surface of PSAs.
The pBA 25 particles cannot be significantly extended due to the extensive polymer chain cross-linking, and so the film fails much sooner than does PSA2, which is designed to allow for extension during fibrillation. The increased modulus (at least in the surface region) for the stratified sample can be seen by the gradient of the initial slope in Figure 6. The application of the adhesive will dictate the trade-off between having a high plateau stress and long extension during fibrillation.
Stratification of Viscoelastic Particles (pBA 0 ). Next, we will present data from a mixture using small pBA 0 particles, which are viscoelastic, because no cross-linker has been added. For the pBA 0 + PSA2 mixtures, AFM imaging shows that particles readily coalesce to form a smooth cohesive film surface, with no visible particle boundaries. This renders AFM    Figure 8a show differences in the deuterium distribution as the values of Pe S are varied. The same normalization procedure as for previous samples was used. Full spectra of the raw data, without normalization, are presented in Figure S2. Starting with Pe S = 3, there are relatively few D counts at the energy corresponding to the surface. A steadily increasing number of counts is seen with decreasing energy, suggesting that D increases with depth. Indeed, in Figure 8b, the fitted D depth profile fluctuates but remains consistently low up to depths of 1000 nm. No surface enrichment of deuterium, and by extension the small pBA 0 particles, is found, which is consistent with the diffusiophoresis model in Table 3.
The other two samples, Pe S = 22 and 95, have higher D counts at the energy for the surface recoils. Qualitatively, these represent an enrichment of deuterium near the top surface of the film, with a lower amount deeper into the film. The fitted depth profiles (Figure 8b) show that both samples have a thin layer composed of pure deuterated pBA, corresponding to a D mole fraction of 0.43. For Pe S = 95, this layer is 23 nm thick, and for Pe S = 22 it is 37 nm thick. Below this layer, the D mole fraction drops to 0.05. The layers enriched in deuterated pBA 0 are slightly subsurface, below a layer of pure, nondeuterated PSA2, which yields a three-layered structure. First, there is a layer of the larger component (PSA2), followed by a layer of the small particles (pBA 0 ), and then finally a random mixture of large and small particles. This result has been observed elsewhere 34,56 and is attributed to a layer of large particles becoming initially trapped at the air/film interface, with smallon-top stratification then occurring below this first layer.
As shown in Figure 8b, the layer thicknesses in the ERD best-fit models are as thin as 40 nm, which is less than the size of an individual pBA 0 particle whose radius is 60 nm. For this mixture, obtaining such a distinct layer of the small component is not realistic, given the ease with which pBA 0 particles will deform and coalesce. Both large and small components in this mixture will have an interfacial width, which also explains the lack of clearly distinguishable pBA 0 layers in the ERD depth profiles. Crucially, the ERD show that the extent of stratification increases as the Pe S is increased.
ERD is only able to probe to a depth of 1 or 2 μm from the surface, but we have successfully resolved sublayers on the order of 40 nm. By contrast, small-angle X-ray scattering (SAXS) using a microbeam has been used to obtain concentration profiles through stratified films up to several 100 μm 56,57 thick, although it does not offer the high resolution of ERD (on the order of tens of nanometers 58−60 ). Similarly, Raman mapping 31 provides depth profiles over large distances but without the high resolution obtained with ERD.
Probe Tack Adhesion. Probe tack curves for the mixture film formed with three different Pe S are presented in Figure 9, in comparison to PSA2. In all cases, a reasonable extension of the fibrils is obtained as is revealed by the long plateau length. The values of σ plateau are consistently higher for the mixture than for PSA2, regardless of the value of Pe S . As such, this parameter shows an effect of a composite but does not indicate an effect of stratification itself. The addition of the pBA 0 particles with no added cross-linker have a reinforcing effect on the fibrils, but the effect on σ plateau is less than found when elastic, cross-linked particles (pBA 25 ) were added.
The strain at failure, ϵ failure , is found to increase with increasing Pe S , as is shown in Figure 10b. Drawing on the rheological data presented in Table 2, it is not expected that a random mixture of PSA2 and pBA 0 will fibrillate farther than the PSA2 on its own. The value of tan(δ)/G′ of 1.4 × 10 −6 for the mixture falls between the values for the components, PSA2 and pBA 0 . It is therefore understandable that the mixture does not fibrillate more than PSA2. Fibril extension is increased with increasing values of Pe S , for which stratification has been established. There is some benefit from the surface enrichment of the mixture with more liquid-like pBA 0 particles, but ϵ failure does not exceed what is found for PSA2.
The greater σ plateau for the PSA mixtures leads to a greater value for W adh when Pe S = 95 and 22 (but not when Pe S = 3) in comparison to PSA2. Considering the ERD depth profiles, it can be inferred that stratification of the viscoleastic pBA 0 particles, as was found for Pe S = 95 and 22, translates to a greater W adh , as shown in Figure 9a. In addition to the effects of a surface layer, there is likely an effect of the viscoelastic properties of the composite, as shown in Table 2. The G′ for the mixture (0.42 MPa) is larger than for the components on their own, which could lead to a greater stress for fibril extension.

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Comparison of the ERD data reveals that the stratified layer is much thicker for the highly cross-linked pBA 25 particles than for the pBA 0 particles presented in this section. Differences in adhesion between the mixed components could have an effect on the stratification. pBA 0 particles are more prone to deformation than pBA 25 , meaning they will experience flatfaced contact with the deforming PSA2 particles. There is likely to be some adhesion between the deforming spheres. Adhesion at the contact points between soft particles might restrict the free diffusion of the particles, thereby inhibiting the stratification into two layers. pBA 25 particles are solid elastic spheres, which will make only a point contact with other particles and be less likely to form strong adhesive contacts. They might be less likely to be restricted in stratification.
Once again, it appears as though having a uniform distribution of the small component (whether it is pBA 0 or pBA 25 ) worsens the adhesive properties of mixed films, whereas having a thin layer stratified near or on the top surface improves the adhesion.

■ CONCLUSIONS
We have shown conclusively that stratification occurs upon the film formation of bimodal colloidal dispersions containing a mixture of small poly(butyl acrylate) and large poly(acrylate) particles, when Pe S is sufficiently high. Tack adhesion properties are modified simply by changing the evaporation rate (via control of the temperature and relative humidity) to achieve a sufficiently fast evaporation of water. PSAs made from the same mixture of colloids had very different adhesive properties, depending on the film formation conditions. As Pe S was increased (at least above 19), enrichment of the small particles at the top surface was found with elastic recoil detection, to depths of 1 μm. Surface coverage or surface enrichment of small particles was shown with atomic force microscopy. Adhesive performance was improved, achieving a W adh greater than that of the plain adhesive, observed in tack tests, as well as tunable failure strain, ϵ failure , arising from greater fibril extension with increasing Pe S .
Our results are in agreement with prior experimental work studying stratification in bimodal colloidal films 30,34 and with investigations showing the benefits of bilayer systems with a gradient in properties, 13−17 in particular the benefit of using a two-layered structure with a thin elastic surface. 13,17 The stratification of the elastic pBA 25 particles lead to a significantly higher plateau stress without sacrificing too much of the extension during fibrillation. As such, W adh was greater than for the two individual components in the mixture.
Previous investigations achieved two layers via successive depositions, whereas in this present research we applied diffusiophoresis-driven stratification to design single deposition films with a gradient in properties, leading to improved adhesion properties. The strategy presented here could be extended to manufacture adhesives with a nontacky surface on top of an adhesive sublayer. Stratification of PSAs during the film deposition could lead to reduced production costs because of the shorter times and less energy required for manufacturing.

Materials.
For the large component, we used a low-T g commercial adhesive (named "PSA2" in this paper) derived from monomers of butyl acrylate and ethyl acrylate, synthesized by emulsion polymerization and received from Synthomer plc. For the small component, we used (non)cross-linked poly(butyl acrylate). Ethylene glycol dimethacrylate (EGDMA), sodium dodecyl sulfonate (SDS), potassium persulfate (KPS), acetone, isopropanol, and 1 M potassium hydroxide (KOH) were purchased from Sigma-Aldrich. Deuterated nbutyl acrylate (d9-nBA) was purchased from Polymer Source, Inc. All chemicals were used as received.
Synthesis of Poly(butyl acrylate) Particles. Prior to each synthesis, a round-bottom flask was thoroughly cleaned by consecutively adding detergent, acetone, and isopropanol. Subsequently, the inner glass surface was etched by 0.1 M potassium hydroxide solution for 3 h and afterward flushed with ample Milli-Q water. Poly(nBA) colloids were synthesized according to a one-step emulsion polymerization. The particles called pBA 25 were made with the addition of EGDMA as a covalent cross-linker at a concentration of 25 mol % calculated as nEGDMA/(nEGDMA + nnBA), where n is the number of moles. The particles called pBA 0 contained no EGDMA.
For the nondeuterated, cross-linked latices (pBA 25 ), 75 g of ingredients was mixed in a 25 mL round-bottom flask containing a 15 × 6 mm 2 (l × w) oval Teflon-coated magnetic stirring bar. First, 6.3 mg of SDS was dissolved in 6.42 g of Milli-Q water by magnetic stirring to provide particle stabilization and fine-tuning of the size. Then, a total of 1.93 g of nBA and the cross-linker EGDMA were homogeneously mixed in a different vial and slowly added on top of the aqueous solution. Subsequently, the flask was sealed with a rubber septum. Oxygen was expelled from the reaction mixture by flushing and bubbling dry nitrogen for 15 min using a long injection needle, while stirring at 150 rpm, followed by 5 min at 60°C. Finally, a solution of 158 mg of the thermally decomposing initiator KPS in 3.7 g of Milli-Q water was injected into the water phase using a long needle, after which the nitrogen inlet and outlet were removed. The reaction was continued for 20 h at 60°C while stirring at 150 rpm. The final colloidal dispersions typically had a solids content of 20 wt %. The nondeuterated latexes were used for polymer characterization because the deuterium-labeled equivalents were produced in small volumes.
The synthesis protocol for the deuterated latices was identical except for the volumes due to the limited quantity of d9-nBA. Specifically, a 25 mL round-bottom flask was used, containing a 15 × 6 mm 2 stirring bar, in which 6.3 mg of SDS and 6.42 g of Milli-Q water were mixed, and a total of 1.93 g of d9-nBA and EGDMA were added. Note that the higher density of d 9 -nBA compared to nondeuterated nBA caused the monomer to sediment to the bottom at room temperature, yet at 60°C, its density was lower than that of the aqueous phase, causing migration to the top�an essential requirement for well-controlled emulsion polymerization.
Particle Characterization. Particle sizes were determined via dynamic light scattering (DLS). Measurements of the diluted samples were performed on a Malvern Zetasizer Nanoseries (Nano S, ZEN1600), using a 4 mW 632.8 nm He−Ne red laser and an avalanche photodiode detector measuring light intensity at a detection angle of 173°. Glass transition temperatures were determined using differential scanning calorimetry (DSC) using a TA Instruments Discovery DSC 250 (Newcastle, DE). 75 μL of the wet samples (10 wt % solids) was drop-cast into pans and dried on a hot plate at 60°C , such that the dry polymer (mass of 6−8 mg) was analyzed. A heat/cool/heat cycle was used, with a heating rate of 20°C min −1 over a range from −80 to 80°C. The T g was determined from the second heating curve. The relative particle sizes presented in Figure 1 provide size ratios of α = 5.5 for the mixture with pBA 0 small particles, and α = 6.5 for pBA 25 .
Polymer Characterization. Molecular weights were determined by gel permeation chromatography (GPC). GPC analysis was performed on a Viscotek GPCMax VE 2001, which has three linear columns (7.5 × 300 mm 2 PLgel mixed-D) operating at 35°C and a flow rate of 1.0 mL/min with tetrahydrofuran (THF) as a mobile phase. PMMA standards were used to calibrate the GPC. Before injection, samples (2−4 mg/mL) were dissolved in THF overnight and filtered through 0.2 μm regenerated cellulose syringe filters.
To determine gel contents, 1 mm thick copolymer films with an initial weight of W 1 were placed into cellulose extraction thimbles, using a Soxhlet extraction method in boiling THF for 24 h. The insoluble copolymer film was dried overnight in a vacuum oven at 40°C and weighed (W 2 ). The gel content, ϕ gel , was calculated as The z-average values of the particle radius, R, are presented alongside values of the cross-linker concentration, molecular weight, M w , glass transition temperatures, T g , and size ratios, α, of the samples in Table  1.
Particle Mixing and Film Formation. Mixed samples were stored on a shaker bench for 30 min prior to film casting. The colloidal mixtures were observed to remain stable, with no evidence for depletion flocculation. For IBA and AFM sample preparation, 400 μL was dropped onto 2 cm × 2 cm silicon wafers and spread uniformly on the substrate, yielding an initial wet film thickness, H, of 1 mm. For probe tack samples, 1500 μL was similarly drop-cast onto 2.5 cm × 7.5 cm glass slides, yielding 160 μm thick dry films. Prior to the film casting, the substrates were wiped with acetone and placed in a UV-ozone cleaner for 10 min to increase their hydrophilicity.
To produce a range of Pe S , samples were film formed under different conditions, detailed in Table 4. For film samples dried on the hot plate, the substrates were first allowed to equilibrate on the hot plate for 5 min.
Ion Beam Analysis. Films were analyzed at the Surrey Ion Beam Centre by performing elastic recoil detection, with a 2.6 MeV 4 He + beam incident on the surface at an angle of 75°to the sample normal. The beam had a diameter of approximately 1 mm. An 8 μm thick aluminum range foil was used to filter out any forward scattered 4 He + ions that may be incident on the ERD detector. A total charge of 10 μC of charged particles was collected from each sample. The detector geometry is shown in Figure S3 (Supporting Information). ERD spectra were analyzed and modeled using SIMNRA software, 61 in which a simple (multi)slab model is employed to fit the data to a given film structure and produce a depth profile. 62 To model the raw data, a single slab containing the approximate composition of a random 3:1 mixture of the two components, containing 33.3% C, 48.4% H, 13.3% O, and 5% D, is first used. When necessary to achieve agreement with the data, additional slabs with a different composition are added to the model. The D:H:C:O stoichiometry of the compositions of the slabs was set so that it corresponded to a mixture of deuterated pBA and PSA2. D and H were identified at the film surface through the corresponding energies of their peaks. Although the concentration of deuterium expected for a mixture containing large and small particle dispersions in a ratio of 3:1 is 10 at. %, during the analysis with SIMNRA, 5 at. % was found to be appropriate for all samples. This discrepancy could be due to uncertainty in the mixing process or deuterium losses from the film arising from beam-induced damage.
Atomic Force Microscopy. Images were recorded on a Bruker Dimension Edge with Scan Asyst atomic force microscope, using Bruker's Scan Asyst image optimization technique. This technique is a type of Peak Force Tapping that requires minimal user input for parameters, such as the set point, because they are automatically adjusted by a feedback loop to optimize the image, based on the information received about the sample surface. Height and adhesion maps are provided, in which height images provide topographic information, and adhesion images provide the relative tip−sample detachment force across the sample surface and is well described by Heinz and Hoh. 63 For Scan Asyst imaging, a SCANASYST-AIR silicon tip on a silicon nitride cantilever was used, with a nominal resonant frequency of 70 kHz and a nominal spring constant of 0.4 N/m, as given by the manufacturer. Images were typically obtained using a scanning rate between 0.5 and 1 Hz.
Probe Tack Adhesion. Probe tack adhesion measurements were performed on a testing rig (Texture Analyzer, TA-XT Plus, Stable Micro Systems, Godalming, UK) using a spherical polypropylene probe (1 in. diameter), a load force of 4.9 N, a test speed of 5 mm/s, and a contact time of 1 s.
During a tack test, a spherical probe is brought into contact with an adhesive film and then retracted from the film at a constant speed. The force required to withdraw the probe from the film is obtained as a function of distance and used to produce a stress−strain curve. Several useful parameters can be obtained from the stress−strain curves. By integrating the curve and multiplying by the dry film thickness, the total work of adhesion, W adh , is found. The maximum stress, σ max , is where the tensile load is at a maximum and represents the onset of cavity formation in the film. As the strain increases, these cavities continue to grow until σ plateau at which point lateral growth stops, and continued deformation occurs by elongation of the cavity walls, known as fibrillation. σ plateau is the stress required to stretch the fibrils, taken at the midpoint of the plateau strain. Film failure occurs either because of fibril detachment from the probe or the substrate, or by fracture within the fibrils, and the point at which this happens is defined as ϵ failure . ■ ASSOCIATED CONTENT
Rheology data for PSA2, pBA 0 , and their mixtures; fitted ERD spectra across the energy range; description of ERD experimental setup and energy calibration (PDF)